One known cruise assist control is a vehicle-following control which controls the own vehicle to follow a preceding vehicle traveling in the same lane as the own vehicle from among preceding vehicles traveling ahead of the own vehicle. In such a vehicle-following control, it is important that a vehicle traveling in the same lane as the own vehicle is identified with high accuracy from among preceding vehicles that are detected by, for example, sensors, cameras or the like. Hence, in the conventional technique, a future travel course of the own vehicle is calculated, and a preceding vehicle which is on that future travel course is subjected to a vehicle-following control. Various methods of calculating a future travel course of the own vehicle have been proposed (see, for example, PTL 1). PTL 1 discloses that the trajectory of a preceding vehicle traveling ahead of the own vehicle is stored to calculate a future travel course of the own vehicle using the stored travel path.